src/HOL/Set.thy
changeset 67403 90fe8c635ba0
parent 67401 a82df75b7f85
child 67443 3abf6a722518
equal deleted inserted replaced
67402:b71431a2051e 67403:90fe8c635ba0
    18   and member :: "'a \<Rightarrow> 'a set \<Rightarrow> bool" \<comment> "membership"
    18   and member :: "'a \<Rightarrow> 'a set \<Rightarrow> bool" \<comment> "membership"
    19   where mem_Collect_eq [iff, code_unfold]: "member a (Collect P) = P a"
    19   where mem_Collect_eq [iff, code_unfold]: "member a (Collect P) = P a"
    20     and Collect_mem_eq [simp]: "Collect (\<lambda>x. member x A) = A"
    20     and Collect_mem_eq [simp]: "Collect (\<lambda>x. member x A) = A"
    21 
    21 
    22 notation
    22 notation
    23   member  (infix "\<in>" 50)
    23   member  ("'(\<in>')") and
       
    24   member  ("(_/ \<in> _)" [51, 51] 50)
    24 
    25 
    25 abbreviation not_member
    26 abbreviation not_member
    26   where "not_member x A \<equiv> \<not> (x \<in> A)" \<comment> "non-membership"
    27   where "not_member x A \<equiv> \<not> (x \<in> A)" \<comment> "non-membership"
    27 notation
    28 notation
    28   not_member  (infix "\<notin>" 50)
    29   not_member  ("'(\<notin>')") and
       
    30   not_member  ("(_/ \<notin> _)" [51, 51] 50)
    29 
    31 
    30 notation (ASCII)
    32 notation (ASCII)
    31   member  (infix ":" 50) and
    33   member  ("'(:')") and
    32   not_member  (infix "~:" 50)
    34   member  ("(_/ : _)" [51, 51] 50) and
       
    35   not_member  ("'(~:')") and
       
    36   not_member  ("(_/ ~: _)" [51, 51] 50)
    33 
    37 
    34 
    38 
    35 text \<open>Set comprehensions\<close>
    39 text \<open>Set comprehensions\<close>
    36 
    40 
    37 syntax
    41 syntax